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1.1 bertrand 1: DOUBLE PRECISION FUNCTION ZLANHF( NORM, TRANSR, UPLO, N, A, WORK )
2: *
1.5 ! bertrand 3: * -- LAPACK routine (version 3.3.1) --
1.1 bertrand 4: *
5: * -- Contributed by Fred Gustavson of the IBM Watson Research Center --
6: * -- April 2009 --
7: *
8: * -- LAPACK is a software package provided by Univ. of Tennessee, --
9: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
10: *
11: * .. Scalar Arguments ..
12: CHARACTER NORM, TRANSR, UPLO
13: INTEGER N
14: * ..
15: * .. Array Arguments ..
16: DOUBLE PRECISION WORK( 0: * )
17: COMPLEX*16 A( 0: * )
18: * ..
19: *
20: * Purpose
21: * =======
22: *
23: * ZLANHF returns the value of the one norm, or the Frobenius norm, or
24: * the infinity norm, or the element of largest absolute value of a
25: * complex Hermitian matrix A in RFP format.
26: *
27: * Description
28: * ===========
29: *
30: * ZLANHF returns the value
31: *
32: * ZLANHF = ( max(abs(A(i,j))), NORM = 'M' or 'm'
33: * (
34: * ( norm1(A), NORM = '1', 'O' or 'o'
35: * (
36: * ( normI(A), NORM = 'I' or 'i'
37: * (
38: * ( normF(A), NORM = 'F', 'f', 'E' or 'e'
39: *
40: * where norm1 denotes the one norm of a matrix (maximum column sum),
41: * normI denotes the infinity norm of a matrix (maximum row sum) and
42: * normF denotes the Frobenius norm of a matrix (square root of sum of
43: * squares). Note that max(abs(A(i,j))) is not a matrix norm.
44: *
45: * Arguments
46: * =========
47: *
48: * NORM (input) CHARACTER
49: * Specifies the value to be returned in ZLANHF as described
50: * above.
51: *
52: * TRANSR (input) CHARACTER
53: * Specifies whether the RFP format of A is normal or
54: * conjugate-transposed format.
55: * = 'N': RFP format is Normal
56: * = 'C': RFP format is Conjugate-transposed
57: *
58: * UPLO (input) CHARACTER
59: * On entry, UPLO specifies whether the RFP matrix A came from
60: * an upper or lower triangular matrix as follows:
61: *
62: * UPLO = 'U' or 'u' RFP A came from an upper triangular
63: * matrix
64: *
65: * UPLO = 'L' or 'l' RFP A came from a lower triangular
66: * matrix
67: *
68: * N (input) INTEGER
69: * The order of the matrix A. N >= 0. When N = 0, ZLANHF is
70: * set to zero.
71: *
72: * A (input) COMPLEX*16 array, dimension ( N*(N+1)/2 );
73: * On entry, the matrix A in RFP Format.
74: * RFP Format is described by TRANSR, UPLO and N as follows:
75: * If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even;
76: * K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If
77: * TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A
78: * as defined when TRANSR = 'N'. The contents of RFP A are
79: * defined by UPLO as follows: If UPLO = 'U' the RFP A
80: * contains the ( N*(N+1)/2 ) elements of upper packed A
81: * either in normal or conjugate-transpose Format. If
82: * UPLO = 'L' the RFP A contains the ( N*(N+1) /2 ) elements
83: * of lower packed A either in normal or conjugate-transpose
84: * Format. The LDA of RFP A is (N+1)/2 when TRANSR = 'C'. When
85: * TRANSR is 'N' the LDA is N+1 when N is even and is N when
86: * is odd. See the Note below for more details.
87: * Unchanged on exit.
88: *
89: * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK),
90: * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
91: * WORK is not referenced.
92: *
93: * Further Details
94: * ===============
95: *
96: * We first consider Standard Packed Format when N is even.
97: * We give an example where N = 6.
98: *
99: * AP is Upper AP is Lower
100: *
101: * 00 01 02 03 04 05 00
102: * 11 12 13 14 15 10 11
103: * 22 23 24 25 20 21 22
104: * 33 34 35 30 31 32 33
105: * 44 45 40 41 42 43 44
106: * 55 50 51 52 53 54 55
107: *
108: *
109: * Let TRANSR = 'N'. RFP holds AP as follows:
110: * For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
111: * three columns of AP upper. The lower triangle A(4:6,0:2) consists of
112: * conjugate-transpose of the first three columns of AP upper.
113: * For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
114: * three columns of AP lower. The upper triangle A(0:2,0:2) consists of
115: * conjugate-transpose of the last three columns of AP lower.
116: * To denote conjugate we place -- above the element. This covers the
117: * case N even and TRANSR = 'N'.
118: *
119: * RFP A RFP A
120: *
121: * -- -- --
122: * 03 04 05 33 43 53
123: * -- --
124: * 13 14 15 00 44 54
125: * --
126: * 23 24 25 10 11 55
127: *
128: * 33 34 35 20 21 22
129: * --
130: * 00 44 45 30 31 32
131: * -- --
132: * 01 11 55 40 41 42
133: * -- -- --
134: * 02 12 22 50 51 52
135: *
136: * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
137: * transpose of RFP A above. One therefore gets:
138: *
139: *
140: * RFP A RFP A
141: *
142: * -- -- -- -- -- -- -- -- -- --
143: * 03 13 23 33 00 01 02 33 00 10 20 30 40 50
144: * -- -- -- -- -- -- -- -- -- --
145: * 04 14 24 34 44 11 12 43 44 11 21 31 41 51
146: * -- -- -- -- -- -- -- -- -- --
147: * 05 15 25 35 45 55 22 53 54 55 22 32 42 52
148: *
149: *
150: * We next consider Standard Packed Format when N is odd.
151: * We give an example where N = 5.
152: *
153: * AP is Upper AP is Lower
154: *
155: * 00 01 02 03 04 00
156: * 11 12 13 14 10 11
157: * 22 23 24 20 21 22
158: * 33 34 30 31 32 33
159: * 44 40 41 42 43 44
160: *
161: *
162: * Let TRANSR = 'N'. RFP holds AP as follows:
163: * For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
164: * three columns of AP upper. The lower triangle A(3:4,0:1) consists of
165: * conjugate-transpose of the first two columns of AP upper.
166: * For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
167: * three columns of AP lower. The upper triangle A(0:1,1:2) consists of
168: * conjugate-transpose of the last two columns of AP lower.
169: * To denote conjugate we place -- above the element. This covers the
170: * case N odd and TRANSR = 'N'.
171: *
172: * RFP A RFP A
173: *
174: * -- --
175: * 02 03 04 00 33 43
176: * --
177: * 12 13 14 10 11 44
178: *
179: * 22 23 24 20 21 22
180: * --
181: * 00 33 34 30 31 32
182: * -- --
183: * 01 11 44 40 41 42
184: *
185: * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
186: * transpose of RFP A above. One therefore gets:
187: *
188: *
189: * RFP A RFP A
190: *
191: * -- -- -- -- -- -- -- -- --
192: * 02 12 22 00 01 00 10 20 30 40 50
193: * -- -- -- -- -- -- -- -- --
194: * 03 13 23 33 11 33 11 21 31 41 51
195: * -- -- -- -- -- -- -- -- --
196: * 04 14 24 34 44 43 44 22 32 42 52
197: *
198: * =====================================================================
199: *
200: * .. Parameters ..
201: DOUBLE PRECISION ONE, ZERO
202: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
203: * ..
204: * .. Local Scalars ..
205: INTEGER I, J, IFM, ILU, NOE, N1, K, L, LDA
206: DOUBLE PRECISION SCALE, S, VALUE, AA
207: * ..
208: * .. External Functions ..
209: LOGICAL LSAME
210: INTEGER IDAMAX
211: EXTERNAL LSAME, IDAMAX
212: * ..
213: * .. External Subroutines ..
214: EXTERNAL ZLASSQ
215: * ..
216: * .. Intrinsic Functions ..
217: INTRINSIC ABS, DBLE, MAX, SQRT
218: * ..
219: * .. Executable Statements ..
220: *
221: IF( N.EQ.0 ) THEN
222: ZLANHF = ZERO
223: RETURN
224: END IF
225: *
226: * set noe = 1 if n is odd. if n is even set noe=0
227: *
228: NOE = 1
229: IF( MOD( N, 2 ).EQ.0 )
1.5 ! bertrand 230: $ NOE = 0
1.1 bertrand 231: *
232: * set ifm = 0 when form='C' or 'c' and 1 otherwise
233: *
234: IFM = 1
235: IF( LSAME( TRANSR, 'C' ) )
1.5 ! bertrand 236: $ IFM = 0
1.1 bertrand 237: *
238: * set ilu = 0 when uplo='U or 'u' and 1 otherwise
239: *
240: ILU = 1
241: IF( LSAME( UPLO, 'U' ) )
1.5 ! bertrand 242: $ ILU = 0
1.1 bertrand 243: *
244: * set lda = (n+1)/2 when ifm = 0
245: * set lda = n when ifm = 1 and noe = 1
246: * set lda = n+1 when ifm = 1 and noe = 0
247: *
248: IF( IFM.EQ.1 ) THEN
249: IF( NOE.EQ.1 ) THEN
250: LDA = N
251: ELSE
252: * noe=0
253: LDA = N + 1
254: END IF
255: ELSE
256: * ifm=0
257: LDA = ( N+1 ) / 2
258: END IF
259: *
260: IF( LSAME( NORM, 'M' ) ) THEN
261: *
262: * Find max(abs(A(i,j))).
263: *
264: K = ( N+1 ) / 2
265: VALUE = ZERO
266: IF( NOE.EQ.1 ) THEN
267: * n is odd & n = k + k - 1
268: IF( IFM.EQ.1 ) THEN
269: * A is n by k
270: IF( ILU.EQ.1 ) THEN
271: * uplo ='L'
272: J = 0
273: * -> L(0,0)
274: VALUE = MAX( VALUE, ABS( DBLE( A( J+J*LDA ) ) ) )
275: DO I = 1, N - 1
276: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
277: END DO
278: DO J = 1, K - 1
279: DO I = 0, J - 2
280: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
281: END DO
282: I = J - 1
283: * L(k+j,k+j)
284: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
285: I = J
286: * -> L(j,j)
287: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
288: DO I = J + 1, N - 1
289: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
290: END DO
291: END DO
292: ELSE
293: * uplo = 'U'
294: DO J = 0, K - 2
295: DO I = 0, K + J - 2
296: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
297: END DO
298: I = K + J - 1
299: * -> U(i,i)
300: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
301: I = I + 1
302: * =k+j; i -> U(j,j)
303: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
304: DO I = K + J + 1, N - 1
305: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
306: END DO
307: END DO
308: DO I = 0, N - 2
309: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
310: * j=k-1
311: END DO
312: * i=n-1 -> U(n-1,n-1)
313: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
314: END IF
315: ELSE
316: * xpose case; A is k by n
317: IF( ILU.EQ.1 ) THEN
318: * uplo ='L'
319: DO J = 0, K - 2
320: DO I = 0, J - 1
321: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
322: END DO
323: I = J
324: * L(i,i)
325: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
326: I = J + 1
327: * L(j+k,j+k)
328: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
329: DO I = J + 2, K - 1
330: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
331: END DO
332: END DO
333: J = K - 1
334: DO I = 0, K - 2
335: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
336: END DO
337: I = K - 1
338: * -> L(i,i) is at A(i,j)
339: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
340: DO J = K, N - 1
341: DO I = 0, K - 1
342: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
343: END DO
344: END DO
345: ELSE
346: * uplo = 'U'
347: DO J = 0, K - 2
348: DO I = 0, K - 1
349: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
350: END DO
351: END DO
352: J = K - 1
353: * -> U(j,j) is at A(0,j)
354: VALUE = MAX( VALUE, ABS( DBLE( A( 0+J*LDA ) ) ) )
355: DO I = 1, K - 1
356: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
357: END DO
358: DO J = K, N - 1
359: DO I = 0, J - K - 1
360: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
361: END DO
362: I = J - K
363: * -> U(i,i) at A(i,j)
364: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
365: I = J - K + 1
366: * U(j,j)
367: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
368: DO I = J - K + 2, K - 1
369: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
370: END DO
371: END DO
372: END IF
373: END IF
374: ELSE
375: * n is even & k = n/2
376: IF( IFM.EQ.1 ) THEN
377: * A is n+1 by k
378: IF( ILU.EQ.1 ) THEN
379: * uplo ='L'
380: J = 0
381: * -> L(k,k) & j=1 -> L(0,0)
382: VALUE = MAX( VALUE, ABS( DBLE( A( J+J*LDA ) ) ) )
383: VALUE = MAX( VALUE, ABS( DBLE( A( J+1+J*LDA ) ) ) )
384: DO I = 2, N
385: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
386: END DO
387: DO J = 1, K - 1
388: DO I = 0, J - 1
389: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
390: END DO
391: I = J
392: * L(k+j,k+j)
393: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
394: I = J + 1
395: * -> L(j,j)
396: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
397: DO I = J + 2, N
398: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
399: END DO
400: END DO
401: ELSE
402: * uplo = 'U'
403: DO J = 0, K - 2
404: DO I = 0, K + J - 1
405: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
406: END DO
407: I = K + J
408: * -> U(i,i)
409: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
410: I = I + 1
411: * =k+j+1; i -> U(j,j)
412: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
413: DO I = K + J + 2, N
414: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
415: END DO
416: END DO
417: DO I = 0, N - 2
418: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
419: * j=k-1
420: END DO
421: * i=n-1 -> U(n-1,n-1)
422: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
423: I = N
424: * -> U(k-1,k-1)
425: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
426: END IF
427: ELSE
428: * xpose case; A is k by n+1
429: IF( ILU.EQ.1 ) THEN
430: * uplo ='L'
431: J = 0
432: * -> L(k,k) at A(0,0)
433: VALUE = MAX( VALUE, ABS( DBLE( A( J+J*LDA ) ) ) )
434: DO I = 1, K - 1
435: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
436: END DO
437: DO J = 1, K - 1
438: DO I = 0, J - 2
439: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
440: END DO
441: I = J - 1
442: * L(i,i)
443: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
444: I = J
445: * L(j+k,j+k)
446: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
447: DO I = J + 1, K - 1
448: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
449: END DO
450: END DO
451: J = K
452: DO I = 0, K - 2
453: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
454: END DO
455: I = K - 1
456: * -> L(i,i) is at A(i,j)
457: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
458: DO J = K + 1, N
459: DO I = 0, K - 1
460: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
461: END DO
462: END DO
463: ELSE
464: * uplo = 'U'
465: DO J = 0, K - 1
466: DO I = 0, K - 1
467: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
468: END DO
469: END DO
470: J = K
471: * -> U(j,j) is at A(0,j)
472: VALUE = MAX( VALUE, ABS( DBLE( A( 0+J*LDA ) ) ) )
473: DO I = 1, K - 1
474: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
475: END DO
476: DO J = K + 1, N - 1
477: DO I = 0, J - K - 2
478: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
479: END DO
480: I = J - K - 1
481: * -> U(i,i) at A(i,j)
482: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
483: I = J - K
484: * U(j,j)
485: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
486: DO I = J - K + 1, K - 1
487: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
488: END DO
489: END DO
490: J = N
491: DO I = 0, K - 2
492: VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
493: END DO
494: I = K - 1
495: * U(k,k) at A(i,j)
496: VALUE = MAX( VALUE, ABS( DBLE( A( I+J*LDA ) ) ) )
497: END IF
498: END IF
499: END IF
500: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
1.5 ! bertrand 501: $ ( NORM.EQ.'1' ) ) THEN
1.1 bertrand 502: *
503: * Find normI(A) ( = norm1(A), since A is Hermitian).
504: *
505: IF( IFM.EQ.1 ) THEN
506: * A is 'N'
507: K = N / 2
508: IF( NOE.EQ.1 ) THEN
509: * n is odd & A is n by (n+1)/2
510: IF( ILU.EQ.0 ) THEN
511: * uplo = 'U'
512: DO I = 0, K - 1
513: WORK( I ) = ZERO
514: END DO
515: DO J = 0, K
516: S = ZERO
517: DO I = 0, K + J - 1
518: AA = ABS( A( I+J*LDA ) )
519: * -> A(i,j+k)
520: S = S + AA
521: WORK( I ) = WORK( I ) + AA
522: END DO
523: AA = ABS( DBLE( A( I+J*LDA ) ) )
524: * -> A(j+k,j+k)
525: WORK( J+K ) = S + AA
526: IF( I.EQ.K+K )
1.5 ! bertrand 527: $ GO TO 10
1.1 bertrand 528: I = I + 1
529: AA = ABS( DBLE( A( I+J*LDA ) ) )
530: * -> A(j,j)
531: WORK( J ) = WORK( J ) + AA
532: S = ZERO
533: DO L = J + 1, K - 1
534: I = I + 1
535: AA = ABS( A( I+J*LDA ) )
536: * -> A(l,j)
537: S = S + AA
538: WORK( L ) = WORK( L ) + AA
539: END DO
540: WORK( J ) = WORK( J ) + S
541: END DO
542: 10 CONTINUE
543: I = IDAMAX( N, WORK, 1 )
544: VALUE = WORK( I-1 )
545: ELSE
546: * ilu = 1 & uplo = 'L'
547: K = K + 1
548: * k=(n+1)/2 for n odd and ilu=1
549: DO I = K, N - 1
550: WORK( I ) = ZERO
551: END DO
552: DO J = K - 1, 0, -1
553: S = ZERO
554: DO I = 0, J - 2
555: AA = ABS( A( I+J*LDA ) )
556: * -> A(j+k,i+k)
557: S = S + AA
558: WORK( I+K ) = WORK( I+K ) + AA
559: END DO
560: IF( J.GT.0 ) THEN
561: AA = ABS( DBLE( A( I+J*LDA ) ) )
562: * -> A(j+k,j+k)
563: S = S + AA
564: WORK( I+K ) = WORK( I+K ) + S
565: * i=j
566: I = I + 1
567: END IF
568: AA = ABS( DBLE( A( I+J*LDA ) ) )
569: * -> A(j,j)
570: WORK( J ) = AA
571: S = ZERO
572: DO L = J + 1, N - 1
573: I = I + 1
574: AA = ABS( A( I+J*LDA ) )
575: * -> A(l,j)
576: S = S + AA
577: WORK( L ) = WORK( L ) + AA
578: END DO
579: WORK( J ) = WORK( J ) + S
580: END DO
581: I = IDAMAX( N, WORK, 1 )
582: VALUE = WORK( I-1 )
583: END IF
584: ELSE
585: * n is even & A is n+1 by k = n/2
586: IF( ILU.EQ.0 ) THEN
587: * uplo = 'U'
588: DO I = 0, K - 1
589: WORK( I ) = ZERO
590: END DO
591: DO J = 0, K - 1
592: S = ZERO
593: DO I = 0, K + J - 1
594: AA = ABS( A( I+J*LDA ) )
595: * -> A(i,j+k)
596: S = S + AA
597: WORK( I ) = WORK( I ) + AA
598: END DO
599: AA = ABS( DBLE( A( I+J*LDA ) ) )
600: * -> A(j+k,j+k)
601: WORK( J+K ) = S + AA
602: I = I + 1
603: AA = ABS( DBLE( A( I+J*LDA ) ) )
604: * -> A(j,j)
605: WORK( J ) = WORK( J ) + AA
606: S = ZERO
607: DO L = J + 1, K - 1
608: I = I + 1
609: AA = ABS( A( I+J*LDA ) )
610: * -> A(l,j)
611: S = S + AA
612: WORK( L ) = WORK( L ) + AA
613: END DO
614: WORK( J ) = WORK( J ) + S
615: END DO
616: I = IDAMAX( N, WORK, 1 )
617: VALUE = WORK( I-1 )
618: ELSE
619: * ilu = 1 & uplo = 'L'
620: DO I = K, N - 1
621: WORK( I ) = ZERO
622: END DO
623: DO J = K - 1, 0, -1
624: S = ZERO
625: DO I = 0, J - 1
626: AA = ABS( A( I+J*LDA ) )
627: * -> A(j+k,i+k)
628: S = S + AA
629: WORK( I+K ) = WORK( I+K ) + AA
630: END DO
631: AA = ABS( DBLE( A( I+J*LDA ) ) )
632: * -> A(j+k,j+k)
633: S = S + AA
634: WORK( I+K ) = WORK( I+K ) + S
635: * i=j
636: I = I + 1
637: AA = ABS( DBLE( A( I+J*LDA ) ) )
638: * -> A(j,j)
639: WORK( J ) = AA
640: S = ZERO
641: DO L = J + 1, N - 1
642: I = I + 1
643: AA = ABS( A( I+J*LDA ) )
644: * -> A(l,j)
645: S = S + AA
646: WORK( L ) = WORK( L ) + AA
647: END DO
648: WORK( J ) = WORK( J ) + S
649: END DO
650: I = IDAMAX( N, WORK, 1 )
651: VALUE = WORK( I-1 )
652: END IF
653: END IF
654: ELSE
655: * ifm=0
656: K = N / 2
657: IF( NOE.EQ.1 ) THEN
658: * n is odd & A is (n+1)/2 by n
659: IF( ILU.EQ.0 ) THEN
660: * uplo = 'U'
661: N1 = K
662: * n/2
663: K = K + 1
664: * k is the row size and lda
665: DO I = N1, N - 1
666: WORK( I ) = ZERO
667: END DO
668: DO J = 0, N1 - 1
669: S = ZERO
670: DO I = 0, K - 1
671: AA = ABS( A( I+J*LDA ) )
672: * A(j,n1+i)
673: WORK( I+N1 ) = WORK( I+N1 ) + AA
674: S = S + AA
675: END DO
676: WORK( J ) = S
677: END DO
678: * j=n1=k-1 is special
679: S = ABS( DBLE( A( 0+J*LDA ) ) )
680: * A(k-1,k-1)
681: DO I = 1, K - 1
682: AA = ABS( A( I+J*LDA ) )
683: * A(k-1,i+n1)
684: WORK( I+N1 ) = WORK( I+N1 ) + AA
685: S = S + AA
686: END DO
687: WORK( J ) = WORK( J ) + S
688: DO J = K, N - 1
689: S = ZERO
690: DO I = 0, J - K - 1
691: AA = ABS( A( I+J*LDA ) )
692: * A(i,j-k)
693: WORK( I ) = WORK( I ) + AA
694: S = S + AA
695: END DO
696: * i=j-k
697: AA = ABS( DBLE( A( I+J*LDA ) ) )
698: * A(j-k,j-k)
699: S = S + AA
700: WORK( J-K ) = WORK( J-K ) + S
701: I = I + 1
702: S = ABS( DBLE( A( I+J*LDA ) ) )
703: * A(j,j)
704: DO L = J + 1, N - 1
705: I = I + 1
706: AA = ABS( A( I+J*LDA ) )
707: * A(j,l)
708: WORK( L ) = WORK( L ) + AA
709: S = S + AA
710: END DO
711: WORK( J ) = WORK( J ) + S
712: END DO
713: I = IDAMAX( N, WORK, 1 )
714: VALUE = WORK( I-1 )
715: ELSE
716: * ilu=1 & uplo = 'L'
717: K = K + 1
718: * k=(n+1)/2 for n odd and ilu=1
719: DO I = K, N - 1
720: WORK( I ) = ZERO
721: END DO
722: DO J = 0, K - 2
723: * process
724: S = ZERO
725: DO I = 0, J - 1
726: AA = ABS( A( I+J*LDA ) )
727: * A(j,i)
728: WORK( I ) = WORK( I ) + AA
729: S = S + AA
730: END DO
731: AA = ABS( DBLE( A( I+J*LDA ) ) )
732: * i=j so process of A(j,j)
733: S = S + AA
734: WORK( J ) = S
735: * is initialised here
736: I = I + 1
737: * i=j process A(j+k,j+k)
738: AA = ABS( DBLE( A( I+J*LDA ) ) )
739: S = AA
740: DO L = K + J + 1, N - 1
741: I = I + 1
742: AA = ABS( A( I+J*LDA ) )
743: * A(l,k+j)
744: S = S + AA
745: WORK( L ) = WORK( L ) + AA
746: END DO
747: WORK( K+J ) = WORK( K+J ) + S
748: END DO
749: * j=k-1 is special :process col A(k-1,0:k-1)
750: S = ZERO
751: DO I = 0, K - 2
752: AA = ABS( A( I+J*LDA ) )
753: * A(k,i)
754: WORK( I ) = WORK( I ) + AA
755: S = S + AA
756: END DO
757: * i=k-1
758: AA = ABS( DBLE( A( I+J*LDA ) ) )
759: * A(k-1,k-1)
760: S = S + AA
761: WORK( I ) = S
762: * done with col j=k+1
763: DO J = K, N - 1
764: * process col j of A = A(j,0:k-1)
765: S = ZERO
766: DO I = 0, K - 1
767: AA = ABS( A( I+J*LDA ) )
768: * A(j,i)
769: WORK( I ) = WORK( I ) + AA
770: S = S + AA
771: END DO
772: WORK( J ) = WORK( J ) + S
773: END DO
774: I = IDAMAX( N, WORK, 1 )
775: VALUE = WORK( I-1 )
776: END IF
777: ELSE
778: * n is even & A is k=n/2 by n+1
779: IF( ILU.EQ.0 ) THEN
780: * uplo = 'U'
781: DO I = K, N - 1
782: WORK( I ) = ZERO
783: END DO
784: DO J = 0, K - 1
785: S = ZERO
786: DO I = 0, K - 1
787: AA = ABS( A( I+J*LDA ) )
788: * A(j,i+k)
789: WORK( I+K ) = WORK( I+K ) + AA
790: S = S + AA
791: END DO
792: WORK( J ) = S
793: END DO
794: * j=k
795: AA = ABS( DBLE( A( 0+J*LDA ) ) )
796: * A(k,k)
797: S = AA
798: DO I = 1, K - 1
799: AA = ABS( A( I+J*LDA ) )
800: * A(k,k+i)
801: WORK( I+K ) = WORK( I+K ) + AA
802: S = S + AA
803: END DO
804: WORK( J ) = WORK( J ) + S
805: DO J = K + 1, N - 1
806: S = ZERO
807: DO I = 0, J - 2 - K
808: AA = ABS( A( I+J*LDA ) )
809: * A(i,j-k-1)
810: WORK( I ) = WORK( I ) + AA
811: S = S + AA
812: END DO
813: * i=j-1-k
814: AA = ABS( DBLE( A( I+J*LDA ) ) )
815: * A(j-k-1,j-k-1)
816: S = S + AA
817: WORK( J-K-1 ) = WORK( J-K-1 ) + S
818: I = I + 1
819: AA = ABS( DBLE( A( I+J*LDA ) ) )
820: * A(j,j)
821: S = AA
822: DO L = J + 1, N - 1
823: I = I + 1
824: AA = ABS( A( I+J*LDA ) )
825: * A(j,l)
826: WORK( L ) = WORK( L ) + AA
827: S = S + AA
828: END DO
829: WORK( J ) = WORK( J ) + S
830: END DO
831: * j=n
832: S = ZERO
833: DO I = 0, K - 2
834: AA = ABS( A( I+J*LDA ) )
835: * A(i,k-1)
836: WORK( I ) = WORK( I ) + AA
837: S = S + AA
838: END DO
839: * i=k-1
840: AA = ABS( DBLE( A( I+J*LDA ) ) )
841: * A(k-1,k-1)
842: S = S + AA
843: WORK( I ) = WORK( I ) + S
844: I = IDAMAX( N, WORK, 1 )
845: VALUE = WORK( I-1 )
846: ELSE
847: * ilu=1 & uplo = 'L'
848: DO I = K, N - 1
849: WORK( I ) = ZERO
850: END DO
851: * j=0 is special :process col A(k:n-1,k)
852: S = ABS( DBLE( A( 0 ) ) )
853: * A(k,k)
854: DO I = 1, K - 1
855: AA = ABS( A( I ) )
856: * A(k+i,k)
857: WORK( I+K ) = WORK( I+K ) + AA
858: S = S + AA
859: END DO
860: WORK( K ) = WORK( K ) + S
861: DO J = 1, K - 1
862: * process
863: S = ZERO
864: DO I = 0, J - 2
865: AA = ABS( A( I+J*LDA ) )
866: * A(j-1,i)
867: WORK( I ) = WORK( I ) + AA
868: S = S + AA
869: END DO
870: AA = ABS( DBLE( A( I+J*LDA ) ) )
871: * i=j-1 so process of A(j-1,j-1)
872: S = S + AA
873: WORK( J-1 ) = S
874: * is initialised here
875: I = I + 1
876: * i=j process A(j+k,j+k)
877: AA = ABS( DBLE( A( I+J*LDA ) ) )
878: S = AA
879: DO L = K + J + 1, N - 1
880: I = I + 1
881: AA = ABS( A( I+J*LDA ) )
882: * A(l,k+j)
883: S = S + AA
884: WORK( L ) = WORK( L ) + AA
885: END DO
886: WORK( K+J ) = WORK( K+J ) + S
887: END DO
888: * j=k is special :process col A(k,0:k-1)
889: S = ZERO
890: DO I = 0, K - 2
891: AA = ABS( A( I+J*LDA ) )
892: * A(k,i)
893: WORK( I ) = WORK( I ) + AA
894: S = S + AA
895: END DO
896: *
897: * i=k-1
898: AA = ABS( DBLE( A( I+J*LDA ) ) )
899: * A(k-1,k-1)
900: S = S + AA
901: WORK( I ) = S
902: * done with col j=k+1
903: DO J = K + 1, N
904: *
905: * process col j-1 of A = A(j-1,0:k-1)
906: S = ZERO
907: DO I = 0, K - 1
908: AA = ABS( A( I+J*LDA ) )
909: * A(j-1,i)
910: WORK( I ) = WORK( I ) + AA
911: S = S + AA
912: END DO
913: WORK( J-1 ) = WORK( J-1 ) + S
914: END DO
915: I = IDAMAX( N, WORK, 1 )
916: VALUE = WORK( I-1 )
917: END IF
918: END IF
919: END IF
920: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
921: *
922: * Find normF(A).
923: *
924: K = ( N+1 ) / 2
925: SCALE = ZERO
926: S = ONE
927: IF( NOE.EQ.1 ) THEN
928: * n is odd
929: IF( IFM.EQ.1 ) THEN
930: * A is normal & A is n by k
931: IF( ILU.EQ.0 ) THEN
932: * A is upper
933: DO J = 0, K - 3
934: CALL ZLASSQ( K-J-2, A( K+J+1+J*LDA ), 1, SCALE, S )
935: * L at A(k,0)
936: END DO
937: DO J = 0, K - 1
938: CALL ZLASSQ( K+J-1, A( 0+J*LDA ), 1, SCALE, S )
939: * trap U at A(0,0)
940: END DO
941: S = S + S
942: * double s for the off diagonal elements
943: L = K - 1
944: * -> U(k,k) at A(k-1,0)
945: DO I = 0, K - 2
946: AA = DBLE( A( L ) )
947: * U(k+i,k+i)
948: IF( AA.NE.ZERO ) THEN
949: IF( SCALE.LT.AA ) THEN
950: S = ONE + S*( SCALE / AA )**2
951: SCALE = AA
952: ELSE
953: S = S + ( AA / SCALE )**2
954: END IF
955: END IF
956: AA = DBLE( A( L+1 ) )
957: * U(i,i)
958: IF( AA.NE.ZERO ) THEN
959: IF( SCALE.LT.AA ) THEN
960: S = ONE + S*( SCALE / AA )**2
961: SCALE = AA
962: ELSE
963: S = S + ( AA / SCALE )**2
964: END IF
965: END IF
966: L = L + LDA + 1
967: END DO
968: AA = DBLE( A( L ) )
969: * U(n-1,n-1)
970: IF( AA.NE.ZERO ) THEN
971: IF( SCALE.LT.AA ) THEN
972: S = ONE + S*( SCALE / AA )**2
973: SCALE = AA
974: ELSE
975: S = S + ( AA / SCALE )**2
976: END IF
977: END IF
978: ELSE
979: * ilu=1 & A is lower
980: DO J = 0, K - 1
981: CALL ZLASSQ( N-J-1, A( J+1+J*LDA ), 1, SCALE, S )
982: * trap L at A(0,0)
983: END DO
984: DO J = 1, K - 2
985: CALL ZLASSQ( J, A( 0+( 1+J )*LDA ), 1, SCALE, S )
986: * U at A(0,1)
987: END DO
988: S = S + S
989: * double s for the off diagonal elements
990: AA = DBLE( A( 0 ) )
991: * L(0,0) at A(0,0)
992: IF( AA.NE.ZERO ) THEN
993: IF( SCALE.LT.AA ) THEN
994: S = ONE + S*( SCALE / AA )**2
995: SCALE = AA
996: ELSE
997: S = S + ( AA / SCALE )**2
998: END IF
999: END IF
1000: L = LDA
1001: * -> L(k,k) at A(0,1)
1002: DO I = 1, K - 1
1003: AA = DBLE( A( L ) )
1004: * L(k-1+i,k-1+i)
1005: IF( AA.NE.ZERO ) THEN
1006: IF( SCALE.LT.AA ) THEN
1007: S = ONE + S*( SCALE / AA )**2
1008: SCALE = AA
1009: ELSE
1010: S = S + ( AA / SCALE )**2
1011: END IF
1012: END IF
1013: AA = DBLE( A( L+1 ) )
1014: * L(i,i)
1015: IF( AA.NE.ZERO ) THEN
1016: IF( SCALE.LT.AA ) THEN
1017: S = ONE + S*( SCALE / AA )**2
1018: SCALE = AA
1019: ELSE
1020: S = S + ( AA / SCALE )**2
1021: END IF
1022: END IF
1023: L = L + LDA + 1
1024: END DO
1025: END IF
1026: ELSE
1027: * A is xpose & A is k by n
1028: IF( ILU.EQ.0 ) THEN
1.5 ! bertrand 1029: * A**H is upper
1.1 bertrand 1030: DO J = 1, K - 2
1031: CALL ZLASSQ( J, A( 0+( K+J )*LDA ), 1, SCALE, S )
1032: * U at A(0,k)
1033: END DO
1034: DO J = 0, K - 2
1035: CALL ZLASSQ( K, A( 0+J*LDA ), 1, SCALE, S )
1036: * k by k-1 rect. at A(0,0)
1037: END DO
1038: DO J = 0, K - 2
1039: CALL ZLASSQ( K-J-1, A( J+1+( J+K-1 )*LDA ), 1,
1.5 ! bertrand 1040: $ SCALE, S )
1.1 bertrand 1041: * L at A(0,k-1)
1042: END DO
1043: S = S + S
1044: * double s for the off diagonal elements
1045: L = 0 + K*LDA - LDA
1046: * -> U(k-1,k-1) at A(0,k-1)
1047: AA = DBLE( A( L ) )
1048: * U(k-1,k-1)
1049: IF( AA.NE.ZERO ) THEN
1050: IF( SCALE.LT.AA ) THEN
1051: S = ONE + S*( SCALE / AA )**2
1052: SCALE = AA
1053: ELSE
1054: S = S + ( AA / SCALE )**2
1055: END IF
1056: END IF
1057: L = L + LDA
1058: * -> U(0,0) at A(0,k)
1059: DO J = K, N - 1
1060: AA = DBLE( A( L ) )
1061: * -> U(j-k,j-k)
1062: IF( AA.NE.ZERO ) THEN
1063: IF( SCALE.LT.AA ) THEN
1064: S = ONE + S*( SCALE / AA )**2
1065: SCALE = AA
1066: ELSE
1067: S = S + ( AA / SCALE )**2
1068: END IF
1069: END IF
1070: AA = DBLE( A( L+1 ) )
1071: * -> U(j,j)
1072: IF( AA.NE.ZERO ) THEN
1073: IF( SCALE.LT.AA ) THEN
1074: S = ONE + S*( SCALE / AA )**2
1075: SCALE = AA
1076: ELSE
1077: S = S + ( AA / SCALE )**2
1078: END IF
1079: END IF
1080: L = L + LDA + 1
1081: END DO
1082: ELSE
1.5 ! bertrand 1083: * A**H is lower
1.1 bertrand 1084: DO J = 1, K - 1
1085: CALL ZLASSQ( J, A( 0+J*LDA ), 1, SCALE, S )
1086: * U at A(0,0)
1087: END DO
1088: DO J = K, N - 1
1089: CALL ZLASSQ( K, A( 0+J*LDA ), 1, SCALE, S )
1090: * k by k-1 rect. at A(0,k)
1091: END DO
1092: DO J = 0, K - 3
1093: CALL ZLASSQ( K-J-2, A( J+2+J*LDA ), 1, SCALE, S )
1094: * L at A(1,0)
1095: END DO
1096: S = S + S
1097: * double s for the off diagonal elements
1098: L = 0
1099: * -> L(0,0) at A(0,0)
1100: DO I = 0, K - 2
1101: AA = DBLE( A( L ) )
1102: * L(i,i)
1103: IF( AA.NE.ZERO ) THEN
1104: IF( SCALE.LT.AA ) THEN
1105: S = ONE + S*( SCALE / AA )**2
1106: SCALE = AA
1107: ELSE
1108: S = S + ( AA / SCALE )**2
1109: END IF
1110: END IF
1111: AA = DBLE( A( L+1 ) )
1112: * L(k+i,k+i)
1113: IF( AA.NE.ZERO ) THEN
1114: IF( SCALE.LT.AA ) THEN
1115: S = ONE + S*( SCALE / AA )**2
1116: SCALE = AA
1117: ELSE
1118: S = S + ( AA / SCALE )**2
1119: END IF
1120: END IF
1121: L = L + LDA + 1
1122: END DO
1123: * L-> k-1 + (k-1)*lda or L(k-1,k-1) at A(k-1,k-1)
1124: AA = DBLE( A( L ) )
1125: * L(k-1,k-1) at A(k-1,k-1)
1126: IF( AA.NE.ZERO ) THEN
1127: IF( SCALE.LT.AA ) THEN
1128: S = ONE + S*( SCALE / AA )**2
1129: SCALE = AA
1130: ELSE
1131: S = S + ( AA / SCALE )**2
1132: END IF
1133: END IF
1134: END IF
1135: END IF
1136: ELSE
1137: * n is even
1138: IF( IFM.EQ.1 ) THEN
1139: * A is normal
1140: IF( ILU.EQ.0 ) THEN
1141: * A is upper
1142: DO J = 0, K - 2
1143: CALL ZLASSQ( K-J-1, A( K+J+2+J*LDA ), 1, SCALE, S )
1144: * L at A(k+1,0)
1145: END DO
1146: DO J = 0, K - 1
1147: CALL ZLASSQ( K+J, A( 0+J*LDA ), 1, SCALE, S )
1148: * trap U at A(0,0)
1149: END DO
1150: S = S + S
1151: * double s for the off diagonal elements
1152: L = K
1153: * -> U(k,k) at A(k,0)
1154: DO I = 0, K - 1
1155: AA = DBLE( A( L ) )
1156: * U(k+i,k+i)
1157: IF( AA.NE.ZERO ) THEN
1158: IF( SCALE.LT.AA ) THEN
1159: S = ONE + S*( SCALE / AA )**2
1160: SCALE = AA
1161: ELSE
1162: S = S + ( AA / SCALE )**2
1163: END IF
1164: END IF
1165: AA = DBLE( A( L+1 ) )
1166: * U(i,i)
1167: IF( AA.NE.ZERO ) THEN
1168: IF( SCALE.LT.AA ) THEN
1169: S = ONE + S*( SCALE / AA )**2
1170: SCALE = AA
1171: ELSE
1172: S = S + ( AA / SCALE )**2
1173: END IF
1174: END IF
1175: L = L + LDA + 1
1176: END DO
1177: ELSE
1178: * ilu=1 & A is lower
1179: DO J = 0, K - 1
1180: CALL ZLASSQ( N-J-1, A( J+2+J*LDA ), 1, SCALE, S )
1181: * trap L at A(1,0)
1182: END DO
1183: DO J = 1, K - 1
1184: CALL ZLASSQ( J, A( 0+J*LDA ), 1, SCALE, S )
1185: * U at A(0,0)
1186: END DO
1187: S = S + S
1188: * double s for the off diagonal elements
1189: L = 0
1190: * -> L(k,k) at A(0,0)
1191: DO I = 0, K - 1
1192: AA = DBLE( A( L ) )
1193: * L(k-1+i,k-1+i)
1194: IF( AA.NE.ZERO ) THEN
1195: IF( SCALE.LT.AA ) THEN
1196: S = ONE + S*( SCALE / AA )**2
1197: SCALE = AA
1198: ELSE
1199: S = S + ( AA / SCALE )**2
1200: END IF
1201: END IF
1202: AA = DBLE( A( L+1 ) )
1203: * L(i,i)
1204: IF( AA.NE.ZERO ) THEN
1205: IF( SCALE.LT.AA ) THEN
1206: S = ONE + S*( SCALE / AA )**2
1207: SCALE = AA
1208: ELSE
1209: S = S + ( AA / SCALE )**2
1210: END IF
1211: END IF
1212: L = L + LDA + 1
1213: END DO
1214: END IF
1215: ELSE
1216: * A is xpose
1217: IF( ILU.EQ.0 ) THEN
1.5 ! bertrand 1218: * A**H is upper
1.1 bertrand 1219: DO J = 1, K - 1
1220: CALL ZLASSQ( J, A( 0+( K+1+J )*LDA ), 1, SCALE, S )
1221: * U at A(0,k+1)
1222: END DO
1223: DO J = 0, K - 1
1224: CALL ZLASSQ( K, A( 0+J*LDA ), 1, SCALE, S )
1225: * k by k rect. at A(0,0)
1226: END DO
1227: DO J = 0, K - 2
1228: CALL ZLASSQ( K-J-1, A( J+1+( J+K )*LDA ), 1, SCALE,
1.5 ! bertrand 1229: $ S )
1.1 bertrand 1230: * L at A(0,k)
1231: END DO
1232: S = S + S
1233: * double s for the off diagonal elements
1234: L = 0 + K*LDA
1235: * -> U(k,k) at A(0,k)
1236: AA = DBLE( A( L ) )
1237: * U(k,k)
1238: IF( AA.NE.ZERO ) THEN
1239: IF( SCALE.LT.AA ) THEN
1240: S = ONE + S*( SCALE / AA )**2
1241: SCALE = AA
1242: ELSE
1243: S = S + ( AA / SCALE )**2
1244: END IF
1245: END IF
1246: L = L + LDA
1247: * -> U(0,0) at A(0,k+1)
1248: DO J = K + 1, N - 1
1249: AA = DBLE( A( L ) )
1250: * -> U(j-k-1,j-k-1)
1251: IF( AA.NE.ZERO ) THEN
1252: IF( SCALE.LT.AA ) THEN
1253: S = ONE + S*( SCALE / AA )**2
1254: SCALE = AA
1255: ELSE
1256: S = S + ( AA / SCALE )**2
1257: END IF
1258: END IF
1259: AA = DBLE( A( L+1 ) )
1260: * -> U(j,j)
1261: IF( AA.NE.ZERO ) THEN
1262: IF( SCALE.LT.AA ) THEN
1263: S = ONE + S*( SCALE / AA )**2
1264: SCALE = AA
1265: ELSE
1266: S = S + ( AA / SCALE )**2
1267: END IF
1268: END IF
1269: L = L + LDA + 1
1270: END DO
1271: * L=k-1+n*lda
1272: * -> U(k-1,k-1) at A(k-1,n)
1273: AA = DBLE( A( L ) )
1274: * U(k,k)
1275: IF( AA.NE.ZERO ) THEN
1276: IF( SCALE.LT.AA ) THEN
1277: S = ONE + S*( SCALE / AA )**2
1278: SCALE = AA
1279: ELSE
1280: S = S + ( AA / SCALE )**2
1281: END IF
1282: END IF
1283: ELSE
1.5 ! bertrand 1284: * A**H is lower
1.1 bertrand 1285: DO J = 1, K - 1
1286: CALL ZLASSQ( J, A( 0+( J+1 )*LDA ), 1, SCALE, S )
1287: * U at A(0,1)
1288: END DO
1289: DO J = K + 1, N
1290: CALL ZLASSQ( K, A( 0+J*LDA ), 1, SCALE, S )
1291: * k by k rect. at A(0,k+1)
1292: END DO
1293: DO J = 0, K - 2
1294: CALL ZLASSQ( K-J-1, A( J+1+J*LDA ), 1, SCALE, S )
1295: * L at A(0,0)
1296: END DO
1297: S = S + S
1298: * double s for the off diagonal elements
1299: L = 0
1300: * -> L(k,k) at A(0,0)
1301: AA = DBLE( A( L ) )
1302: * L(k,k) at A(0,0)
1303: IF( AA.NE.ZERO ) THEN
1304: IF( SCALE.LT.AA ) THEN
1305: S = ONE + S*( SCALE / AA )**2
1306: SCALE = AA
1307: ELSE
1308: S = S + ( AA / SCALE )**2
1309: END IF
1310: END IF
1311: L = LDA
1312: * -> L(0,0) at A(0,1)
1313: DO I = 0, K - 2
1314: AA = DBLE( A( L ) )
1315: * L(i,i)
1316: IF( AA.NE.ZERO ) THEN
1317: IF( SCALE.LT.AA ) THEN
1318: S = ONE + S*( SCALE / AA )**2
1319: SCALE = AA
1320: ELSE
1321: S = S + ( AA / SCALE )**2
1322: END IF
1323: END IF
1324: AA = DBLE( A( L+1 ) )
1325: * L(k+i+1,k+i+1)
1326: IF( AA.NE.ZERO ) THEN
1327: IF( SCALE.LT.AA ) THEN
1328: S = ONE + S*( SCALE / AA )**2
1329: SCALE = AA
1330: ELSE
1331: S = S + ( AA / SCALE )**2
1332: END IF
1333: END IF
1334: L = L + LDA + 1
1335: END DO
1336: * L-> k - 1 + k*lda or L(k-1,k-1) at A(k-1,k)
1337: AA = DBLE( A( L ) )
1338: * L(k-1,k-1) at A(k-1,k)
1339: IF( AA.NE.ZERO ) THEN
1340: IF( SCALE.LT.AA ) THEN
1341: S = ONE + S*( SCALE / AA )**2
1342: SCALE = AA
1343: ELSE
1344: S = S + ( AA / SCALE )**2
1345: END IF
1346: END IF
1347: END IF
1348: END IF
1349: END IF
1350: VALUE = SCALE*SQRT( S )
1351: END IF
1352: *
1353: ZLANHF = VALUE
1354: RETURN
1355: *
1356: * End of ZLANHF
1357: *
1358: END